Properties of Subtraction

Date: 04/08/97 at 17:22:35
From: kim Sebastian
Subject: Properties of Subtraction
1) Is subtraction commutative? How can this be justified?
2) Is subtraction associative? and how can this be justified?
Thanks,
Mrs. Sebastian

Date: 04/09/97 at 15:01:08
From: Doctor Mike
Subject: Re: Properties of Subtraction
Dear Mrs. Sebastian,
This is an interesting question, and the answer is subtle, but
there IS an answer. It's sort of a "yes and no" answer. Here goes.
1. Subtraction is NOT commutative. If you evaluate 3-2 and 2-3
you get +1 and -1, respectively. NOT the same thing.
2. Subtraction is NOT associative. If you evaluate (3-2)-1 and
3-(2-1) you get 0 and 2, respectively. NOT the same thing.
3. However, **addition** is commutative for all numbers, even
including negative numbers. An example related to (1.) is:
3 + -2 = -2 + 3 = +1
4. Also, **addition** is associative for all numbers, even the
negative numbers. An example related to (2.) above is:
(3 + -2) + -1 = 3 + (-2 + -1) = 0
To see this better, evaluate what is inside parentheses, getting
( 1 ) + -1 = 3 + ( -3 ) = 0
I hope this helps. Feel free to write back if you're not yet
completely comfortable with this. I'm glad you want to get it.
-Doctor Mike, The Math Forum
Check out our web site! http://mathforum.org/dr.math/